Mental healthcare of elderly people is a common problem in advanced countries. Recently, high technology has developed robots for use not only in factories but also for our living environment. In particular, human-interactive robots for psychological enrichment, which provide services by interacting with humans while stimulating their minds, are rapidly spreading. Such robots not only simply entertain but also render assistance, guide, provide therapy, educate, enable communication, and so on. Robot therapy, which uses robots as a substitution for animals in animal-assisted therapy and activity, is a new application of robots and is attracting the attention of many researchers and psychologists. The seal robot named Paro was developed especially for robot therapy and was used at hospitals and facilities for elderly people in several countries. Recent research has revealed that robot therapy has the same effects on people as animal therapy. In addition, it is being recognized as a new method of mental healthcare for elderly people. In this mini review, we introduce the merits and demerits of animal therapy. Then we explain the human-interactive robot for psychological enrichment, the required functions for therapeutic robots, and the seal robot. Finally, we provide examples of robot therapy for elderly people, including dementia patients.